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Factors of 2400

Factors of 2400 are the list of integers that can be evenly divided into 2400. There are total 36 factors of 2400, of which 2, 3, 5 are its prime factors. The Prime Factorization of 2400 is 25 × 31 × 52.

  • All Factors of 2400: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
  • Prime Factors of 2400: 2, 3, 5
  • Prime Factorization of 2400: 25 × 31 × 52
  • Sum of Factors of 2400: 7812
1. What Are the Factors of 2400?
2. Factors of 2400 by Prime Factorization
3. Factors of 2400 in Pairs
4. FAQs on Factors of 2400
Factors of 2400

What are Factors of 2400?

Factors of 2400 are pairs of those numbers whose products result in 2400. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2400?

To find the factors of 2400, we will have to find the list of numbers that would divide 2400 without leaving any remainder.

  • 2400/25 = 96; therefore, 25 is a factor of 2400 and 96 is also a factor of 2400.
  • 2400/50 = 48; therefore, 50 is a factor of 2400 and 48 is also a factor of 2400.
Similarly we can find other factors. Hence, the factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400.

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Factors of 2400 by Prime Factorization

The number 2400 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2400. The first step is to divide the number 2400 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2400 ÷ 2 = 1200
  • 1200 ÷ 2 = 600
  • 600 ÷ 2 = 300
  • 300 ÷ 2 = 150
  • 150 ÷ 2 = 75

Further dividing 75 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 75 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 2400 can be written as 25 × 31 × 52 where 2, 3, 5 are prime.

 

Factors of 2400 in Pairs

Pair factors of 2400 are the pairs of numbers that when multiplied give the product 2400. The factors of 2400 in pairs are:

  • 1 × 2400 = (1, 2400)
  • 2 × 1200 = (2, 1200)
  • 3 × 800 = (3, 800)
  • 4 × 600 = (4, 600)
  • 5 × 480 = (5, 480)
  • 6 × 400 = (6, 400)
  • 8 × 300 = (8, 300)
  • 10 × 240 = (10, 240)
  • 12 × 200 = (12, 200)
  • 15 × 160 = (15, 160)
  • 16 × 150 = (16, 150)
  • 20 × 120 = (20, 120)
  • 24 × 100 = (24, 100)
  • 25 × 96 = (25, 96)
  • 30 × 80 = (30, 80)
  • 32 × 75 = (32, 75)
  • 40 × 60 = (40, 60)
  • 48 × 50 = (48, 50)

Negative pair factors of 2400 are:

  • -1 × -2400 = (-1, -2400)
  • -2 × -1200 = (-2, -1200)
  • -3 × -800 = (-3, -800)
  • -4 × -600 = (-4, -600)
  • -5 × -480 = (-5, -480)
  • -6 × -400 = (-6, -400)
  • -8 × -300 = (-8, -300)
  • -10 × -240 = (-10, -240)
  • -12 × -200 = (-12, -200)
  • -15 × -160 = (-15, -160)
  • -16 × -150 = (-16, -150)
  • -20 × -120 = (-20, -120)
  • -24 × -100 = (-24, -100)
  • -25 × -96 = (-25, -96)
  • -30 × -80 = (-30, -80)
  • -32 × -75 = (-32, -75)
  • -40 × -60 = (-40, -60)
  • -48 × -50 = (-48, -50)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 2400 Solved Examples

  1. Example 1: How many factors are there for 2400?

    Solution:

    The factors of 2400 are too many, therefore if we can find the prime factorization of 2400, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 2400 = 25 × 31 × 52
    Therefore, the total number of factors are (5 + 1) × (1 + 1) × (2 + 1) = 6 × 2 × 3 = 36

  2. Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 2400 and 1867.

    Solution:

    The factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400 and factors of 1867 are 1, 1867.

    Therefore, the Least Common Multiple of 2400 and 1867 is 4480800 and Highest Common Factor (HCF) of 2400 and 1867 is 1.

  3. Example 3: Find if 2, 10, 48, 75, 300, 480, 800 and 2035 are factors of 2400.

    Solution:

    When we divide 2400 by 2035 it leaves a remainder. Therefore, the number 2035 is not a factor of 2400. All numbers except 2035 are factors of 2400.

  4. Example 4: Find the product of all the prime factors of 2400.

    Solution:

    Since, the prime factors of 2400 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 2400

What are the Factors of 2400?

The factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -32, -40, -48, -50, -60, -75, -80, -96, -100, -120, -150, -160, -200, -240, -300, -400, -480, -600, -800, -1200, -2400.

What is the Sum of Factors of 2400?

Sum of all factors of 2400 = (25 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) = 7812

What are the Pair Factors of 2400?

The pair factors of 2400 are (1, 2400), (2, 1200), (3, 800), (4, 600), (5, 480), (6, 400), (8, 300), (10, 240), (12, 200), (15, 160), (16, 150), (20, 120), (24, 100), (25, 96), (30, 80), (32, 75), (40, 60), (48, 50).

What is the Greatest Common Factor of 2400 and 1711?

The factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400 and the factors of 1711 are 1, 29, 59, 1711. 2400 and 1711 have only one common factor which is 1. This implies that 2400 and 1711 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2400 and 1711 is 1.

How Many Factors of 2400 are also Factors of 2137?

Since, the factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400 and factors of 2137 are 1, 2137. Hence, 2400 and 2137 have only one common factor which is 1. Therefore, 2400 and 2137 are co-prime.

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